If randomized to the haplo-cord group, a family member will undergo a stem cell collection. In both arms, subjects will receive a "conditioning regimen" prior to transplantation. The conditioning regimen consists of chemotherapy, which is meant to destroy the cancer cells and suppress the immune system to allow the transplanted cells to grow. Subjects will remain in the hospital until the stem cells are fully recovered, which is usually 4 to 6 weeks after the transplant. Subjects will have bone marrow aspiration and biopsy at 3 weeks, 4 weeks, 2 months, 6 months and 1 year after the transplant and then yearly thereafter. Participation in the study will continue for up to 5 years after transplantation.